{"id":127,"date":"2023-07-16T17:57:55","date_gmt":"2023-07-16T17:57:55","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e4%b8%89%e8%a7%92%e6%81%92%e7%ad%89%e5%bc%8f\/"},"modified":"2023-07-16T17:57:55","modified_gmt":"2023-07-16T17:57:55","slug":"%e4%b8%89%e8%a7%92%e6%81%92%e7%ad%89%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e4%b8%89%e8%a7%92%e6%81%92%e7%ad%89%e5%bc%8f\/","title":{"rendered":"\u4ec0\u4e48\u662f\u4e09\u89d2\u6052\u7b49\u5f0f\uff1f"},"content":{"rendered":"<p><strong>\u4e09\u89d2\u6052\u7b49\u5f0f<\/strong>\u662f\u4e0d\u540c\u4e09\u89d2\u51fd\u6570\u4e4b\u95f4\u7684\u7b49\u5f0f\u3002\u7531\u4e8e\u8fd9\u4e9b\u4e09\u89d2\u7b49\u4ef7\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u4efb\u4f55\u5176\u4ed6\u4e09\u89d2\u6bd4\u63a8\u5bfc\u51fa\u67d0\u4e2a<a href=\"https:\/\/mathority.org\/cn\/\u4e09\u89d2\u6bd4\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u4e09\u89d2\u6bd4<\/a>\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u7406\u89e3\u4e09\u89d2\u6052\u7b49\u5f0f\u7684\u516c\u5f0f\uff0c\u6709\u5fc5\u8981\u77e5\u9053\u8fd9\u4e9b\u6bd4\u7387\u7684\u516c\u5f0f\u3002\u5982\u679c\u60a8\u4e0d\u77e5\u9053\u60a8\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u5efa\u8bae\u60a8\u8bbf\u95ee\u6700\u540e\u4e00\u4e2a\u94fe\u63a5\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Tabla_de_identidades_trigonometricas\">\u4e09\u89d2\u6052\u7b49\u5f0f\u8868<\/span><\/h2>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"301\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formulaire-didentites-trigonometriques.webp\" data-src=\"\" alt=\"\u4e09\u89d2\u6052\u7b49\u5f0f\u5f62\u5f0f\" class=\"wp-image-7444 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Formulario-de-identidades-trigonometricas-800x301.png 800w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Formulario-de-identidades-trigonometricas-500x188.png 500w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Formulario-de-identidades-trigonometricas-768x289.png 768w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Formulario-de-identidades-trigonometricas.png 1173w\" sizes=\"auto, \" srcset=\"\"><figcaption>\u4e09\u89d2\u6052\u7b49\u5f0f\u5f62\u5f0f<\/figcaption><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span id=\"Identidades_trigonometricas_fundamentales\">\u57fa\u672c\u4e09\u89d2\u6052\u7b49\u5f0f<\/span><\/h2>\n<p>\u6709\u4e00\u7cfb\u5217\u57fa\u672c\u4e09\u89d2\u6052\u7b49\u5f0f\u88ab\u8ba4\u4e3a\u662f\u6700\u91cd\u8981\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u4e3a\u5176\u4ed6\u4e09\u89d2\u6052\u7b49\u5f0f\u63d0\u4f9b\u4e86<strong>\u7406\u8bba\u57fa\u7840<\/strong>\u3002\u8fd9\u4e9b\u662f\u6700\u5e38\u89c1\u7684\uff0c\u4e5f\u53ef\u80fd\u662f\u6700\u5bb9\u6613\u8bb0\u4f4f\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u975e\u5e38\u76f4\u89c2\u3002\u8bf7\u8bb0\u4f4f\uff0c\u6240\u6709\u516c\u5f0f\u90fd\u5c06\u57fa\u4e8e\u4e0b\u56fe\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"319\" height=\"248\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/triangle-rectangle.webp\" data-src=\"\" alt=\"\u4e09\u89d2\u5f62 \u957f\u65b9\u5f62\" class=\"wp-image-7379 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\">\u57fa\u672c\u4e09\u89d2\u6052\u7b49\u5f0f<\/h3>\n<p>\u7b2c\u4e00\u4e2a\u6052\u7b49\u5f0f\u662f\u6240\u8c13\u7684<strong>\u57fa\u672c\u4e09\u89d2\u6052\u7b49\u5f0f<\/strong>\uff0c\u4e5f\u79f0\u4e3a\u6b63\u5f26\u548c\u4f59\u5f26\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u4e0b\u9762\u662f\u5176\u6570\u5b66\u8bc1\u660e\uff1asin\u00b2 (\u03b1) + cos\u00b2 (\u03b1) = 1\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"233\" height=\"355\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/preuve-didentite-trigonometrique-fondamentale.webp\" data-src=\"\" alt=\"\u57fa\u672c\u4e09\u89d2\u8eab\u4efd\u8bc1\u660e\" class=\"wp-image-7420 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u5728\u6700\u540e\u4e00\u6b65\u4e2d\uff0c\u6211\u4eec\u57fa\u672c\u4e0a\u5e94\u7528\u6bd5\u8fbe\u54e5\u62c9\u65af\u5b9a\u7406\uff0c\u56e0\u4e3a c\u00b2 = a\u00b2 + b\u00b2\uff0c\u6240\u4ee5\u6211\u4eec\u5269\u4e0b c\u00b2 \/ c\u00b2 \u7b49\u4e8e 1\u3002\u603b\u4e4b\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\uff1a sin\u00b2 (\u03b1) + cos\u00b2 (\u03b1) = 1\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5272\u7ebf\u548c\u6b63\u5207\u7684\u5173\u7cfb\uff08\u5272\u7ebf\u5e73\u65b9\uff09<\/h3>\n<p>\u5176\u6b21\uff0c\u6211\u4eec\u6709\u4e00\u4e2a\u5c06\u6b63\u5207\u4e0e\u6b63\u5207\u8054\u7cfb\u8d77\u6765\u7684\u4e09\u89d2\u6052\u7b49\u5f0f\uff0c\u5176\u8868\u8fbe\u5f0f\u5982\u4e0b\uff1a <strong>sec\u00b2 (\u03b1) = 1 + tan\u00b2 (\u03b1)<\/strong> \u3002\u5728\u4e0b\u56fe\u4e2d\uff0c\u60a8\u53ef\u4ee5\u770b\u5230\u4e00\u4e9b\u6784\u6210\u6b64\u6052\u7b49\u5f0f\u7684\u63d0\u9192\u516c\u5f0f\uff0c\u4ee5\u53ca\u5f97\u51fa\u6700\u7ec8\u516c\u5f0f\u6240\u9700\u9075\u5faa\u7684\u8fc7\u7a0b\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"357\" height=\"637\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/relation-de-preuve-entre-secante-et-tangente.webp\" data-src=\"\" alt=\"\u8bc1\u660e\u5272\u7ebf\u548c\u5207\u7ebf\u4e4b\u95f4\u7684\u5173\u7cfb\" class=\"wp-image-7421 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Demostracion-relacion-entre-secante-y-tangente.png 357w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Demostracion-relacion-entre-secante-y-tangente-280x500.png 280w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4f7f\u7528\u4e09\u89d2\u6bd4\u7387\u516c\u5f0f\u6765\u67e5\u627e\u5176\u4ed6\u6bd4\u7387\u3002\u603b\u4e4b\uff0c\u6211\u4eec\u53ef\u4ee5\u8bf4\uff1asec\u00b2(\u03b1) = 1 + tan\u00b2(\u03b1)\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u4f59\u5272\u548c\u4f59\u5207\u4e4b\u95f4\u7684\u5173\u7cfb\uff08\u4f59\u5272\u5e73\u65b9\uff09<\/h3>\n<p>\u4ece\u4f59\u5272\u548c\u4f59\u5207\u7684\u5b9a\u4e49\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u6b63\u5207\u516c\u5f0f\u7684\u8054\u7cfb\uff0c\u7531\u6b64\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u53e6\u4e00\u4e2a\u4e09\u89d2\u6052\u7b49\u5f0f\uff1a <strong>cosec\u00b2 (\u03b1) = 1 + cotg\u00b2 (\u03b1)<\/strong> \u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"548\" height=\"752\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/relation-de-preuve-entre-cosecante-et-cotangente.webp\" data-src=\"\" alt=\"\u8bc1\u660e\u4f59\u5272\u548c\u4f59\u5207\u5173\u7cfb\" class=\"wp-image-7425 lazyload\" data-srcset=\"https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Demostracion-relacion-entre-cosecante-y-cotangente.png 548w, https:\/\/micalculadoracientifica.com\/wp-content\/uploads\/2022\/03\/Demostracion-relacion-entre-cosecante-y-cotangente-364x500.png 364w\" sizes=\"auto, \" srcset=\"\"><\/figure>\n<\/div>\n<p>\u901a\u8fc7\u8fd9\u4e2a\u6f14\u793a\uff0c\u6211\u4eec\u53ef\u4ee5\u9a8c\u8bc1\uff1acosec\u00b2 (\u03b1) = 1 + cotg\u00b2 (\u03b1)\u3002\u6b64\u5916\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u8fd9\u79cd\u5173\u7cfb\u4e0e\u524d\u4e00\u79cd\u5173\u7cfb\u6709\u4e00\u4e9b\u76f8\u4f3c\u4e4b\u5904\uff0c\u8fd9\u662f\u7531\u4e8e\u6b63\u5207\u548c\u4f59\u5207\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Razones_trigonometricas_del_angulo_suma_y_del_angulo_resta\">\u548c\u89d2\u4e0e\u51cf\u89d2\u7684\u4e09\u89d2\u6bd4<\/span><\/h2>\n<p><strong>\u89d2\u548c\u6216\u89d2\u51cf\u6bd4<\/strong>\u662f\u901a\u8fc7\u8ba1\u7b97\u4e24\u4e2a\u89d2\u5ea6\u76f8\u52a0\u6216\u76f8\u51cf\u7684\u4e09\u89d2\u6bd4\u800c\u83b7\u5f97\u7684\u4e00\u79cd\u6052\u7b49\u5f0f\u3002\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u8981\u8ba1\u7b97 90 + 60 \u7684\u6b63\u5f26\uff0c\u6709\u4e00\u7cfb\u5217\u516c\u5f0f\u53ef\u4ee5\u4f7f\u8fd9\u4e2a\u8ba1\u7b97\u53d8\u5f97\u66f4\u5bb9\u6613\u3002\u4e0b\u9762\u5217\u51fa\u4e86\u8fd9\u79cd\u7c7b\u578b\u7684\u4e09\u89d2\u6052\u7b49\u5f0f\u7684\u6240\u6709\u516c\u5f0f\uff1a<\/p>\n<p class=\"has-text-align-center\">\u89d2\u5ea6\u548c\u7684\u6b63\u5f26\uff1a sin (\u03b1 + <em>\u03b2<\/em> ) = sin (\u03b1) cos ( <em>\u03b2<\/em> ) + cos ( <em>\u03b1<\/em> ) sin ( <em>\u03b2<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u89d2\u5ea6\u51cf\u6cd5\u7684\u6b63\u5f26\uff1asin (\u03b1 \u2013 <em>\u03b2<\/em> ) = sin (\u03b1) cos ( <em>\u03b2<\/em> ) \u2013 cos ( <em>\u03b1<\/em> ) sin ( <em>\u03b2<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u89d2\u5ea6\u548c\u7684\u4f59\u5f26\uff1a cos (\u03b1 + <em>\u03b2<\/em> ) = cos (\u03b1) cos ( <em>\u03b2<\/em> ) \u2013 sin ( <em>\u03b1<\/em> ) sin ( <em>\u03b2<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u89d2\u4f59\u5f26\u51cf\u6cd5\uff1a cos (\u03b1 \u2013 <em>\u03b2<\/em> ) = cos (\u03b1) cos ( <em>\u03b2<\/em> ) + sin ( <em>\u03b1<\/em> ) sin ( <em>\u03b2<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u89d2\u5ea6\u548c\u7684\u6b63\u5207\uff1a tan (\u03b1 + <em>\u03b2<\/em> ) = (tan (\u03b1) + tan ( <em>\u03b2<\/em> )) \u00f7 (1 \u2013 tan (\u03b1) tan ( <em>\u03b2<\/em> ))<\/p>\n<p class=\"has-text-align-center\">\u89d2\u6b63\u5207\u51cf\u6cd5\uff1a tan(\u03b1 \u2013 <em>\u03b2<\/em> ) = (tan(\u03b1) + tan( <em>\u03b2<\/em> )) \u00f7(1 + tan(\u03b1)tan( <em>\u03b2<\/em> ))<\/p>\n<p>\u663e\u7136\uff0c\u8ba1\u7b97 150\u00b0 \u7684\u6b63\u5f26\u6bd4\u4f7f\u7528\u6211\u4eec\u521a\u624d\u89e3\u91ca\u7684\u516c\u5f0f\u8ba1\u7b97 (90\u00b0 + 60\u00b0) \u7684\u6b63\u5f26\u8981\u5bb9\u6613\u3002\u90a3\u4e48\u4e3a\u4ec0\u4e48\u8fd9\u4e9b\u516c\u5f0f\u5f88\u91cd\u8981\u5462\uff1f\u7b54\u6848\u662f\uff0c\u8fd9\u4e9b\u6052\u7b49\u5f0f\u4f7f\u6211\u4eec\u80fd\u591f\u4ece\u66f4\u7b80\u5355\u7684\u89d2\u5ea6\u8ba1\u7b97<strong>\u590d\u6742\u89d2\u5ea6<\/strong>\u7684\u4e09\u89d2\u6bd4\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u8bb0\u4f4f\u4e86\u503c\u5f97\u6ce8\u610f\u7684\uff08\u6700\u76f8\u5173\u7684\uff09\u89d2\u5ea6\u7684\u6bd4\u7387\uff0c\u6211\u4eec\u5c31\u4e0d\u9700\u8981\u4f7f\u7528\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u66f4\u590d\u6742\u7684\u89d2\u5ea6\uff08\u4f8b\u5982 150\u00b0\uff09\u7684\u6bd4\u7387\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Razones_trigonometricas_del_angulo_doble\">\u53cc\u89d2\u4e09\u89d2\u6bd4<\/span><\/h2>\n<p>\u5f53\u6211\u4eec\u60f3\u8981\u8ba1\u7b97<strong>\u53cc\u89d2 (2\u03b1) \u7684\u4e09\u89d2\u6bd4<\/strong>\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e00\u7cfb\u5217\u6052\u7b49\u5f0f\u6765\u5b9e\u73b0\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e0e\u4e0a\u4e00\u8282\u8ba8\u8bba\u7684\u516c\u5f0f\u975e\u5e38\u76f8\u4f3c\u7684\u516c\u5f0f\u6765\u505a\u5230\u8fd9\u4e00\u70b9\u3002\u56e0\u4e3a\uff0c\u5982\u679c\u6211\u4eec\u5c06<em>\u03b2<\/em>\u66f4\u6539\u4e3a \u03b1\uff0c\u5219\u5728\u524d\u9762\u7684\u8868\u8fbe\u5f0f\u4e2d\uff0c\u6211\u4eec\u5269\u4e0b (\u03b1 + \u03b1)\uff0c\u8fd9\u76f8\u5f53\u4e8e (2\u03b1)\u3002\u8003\u8651\u5230\u8fd9\u4e00\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u4ee5\u4e0b\u6052\u7b49\u5f0f\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"172\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/rapports-trigonometriques-a-double-angle.webp\" data-src=\"\" alt=\"\u53cc\u89d2\u4e09\u89d2\u6bd4\" class=\"wp-image-7432 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u60a8\u53ef\u4ee5\u770b\u5230\u4e0b\u9762\u7684\u6f14\u793a\uff1a<\/p>\n<p class=\"has-text-align-center\">\u53cc\u89d2\u7684\u6b63\u5f26\uff1asin(2\u03b1)=sin(\u03b1)cos(\u03b1)+cos(\u03b1)sin(\u03b1)=2sin(\u03b1)cos(\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u53cc\u89d2\u4f59\u5f26\uff1a cos (\u03b1 + <em>\u03b1<\/em> ) = cos (\u03b1) cos ( <em>\u03b1<\/em> ) \u2013 sin ( <em>\u03b1<\/em> ) sin ( <em>\u03b1<\/em> ) = cos\u00b2 (\u03b1) \u2013 sin\u00b2 (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u53cc\u5207\u7ebf\u89d2\uff1a tan (2\u03b1) = 2 tan (\u03b1) \u00f7 (1 \u2013 tan\u00b2 (\u03b1))<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Razones_trigonometricas_del_angulo_mitad\">\u534a\u89d2\u7684\u4e09\u89d2\u6bd4<\/span><\/h2>\n<p>\u6b64\u5916\uff0c\u8fd8\u6709\u4e00\u4e9b\u6052\u7b49\u5f0f\u53ef\u4ee5\u8ba9\u6211\u4eec\u8ba1\u7b97<strong>\u534a\u89d2\u7684\u4e09\u89d2\u6bd4 (\u03b1\/2)<\/strong> \uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"295\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/rapports-trigonometriques-du-demi-angle.webp\" data-src=\"\" alt=\"\u534a\u89d2\u7684\u4e09\u89d2\u6bd4\" class=\"wp-image-7431 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4ee5\u4e0b\u662f\u5df2\u77e5\u7684\u516c\u5f0f\uff1a<\/p>\n<p class=\"has-text-align-center\"> 1 = sin\u00b2( <em>\u03b2<\/em> ) + cos\u00b2( <em>\u03b2<\/em> )<\/p>\n<p class=\"has-text-align-center\"> cos( <em>2\u03b2<\/em> ) = cos\u00b2( <em>\u03b2<\/em> ) \u2013 sin\u00b2( <em>\u03b2<\/em> )<\/p>\n<p>\u5982\u679c\u6211\u4eec\u4f7f<em>\u03b2<\/em> = \u03b1\/2\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5c06\u6b63\u5f26\u60c5\u51b5\u4e0b\u7684\u4e24\u4e2a\u8868\u8fbe\u5f0f\u76f8\u51cf\uff0c\u5728\u4f59\u5f26\u60c5\u51b5\u4e0b\u5c06\u5b83\u4eec\u76f8\u52a0\uff0c\u7136\u540e\u5c06\u5f97\u5230\u7684\u4e24\u4e2a\u516c\u5f0f\uff08\u6b63\u5f26\u516c\u5f0f\u548c\u4f59\u5f26\u516c\u5f0f\uff09\u76f8\u9664\u6765\u8bc1\u660e\u8fd9\u4e9b\u6052\u7b49\u5f0f\u5728\u5207\u7ebf\u7684\u60c5\u51b5\u4e0b\u3002\u7136\u800c\uff0c\u4ecd\u7136\u9700\u8981\u5728\u4e0b\u9762\u83b7\u5f97\u7684\u516c\u5f0f\u4e2d<strong>\u5206\u79bb\u51fa\u6211\u4eec\u60f3\u8981\u8ba1\u7b97\u7684\u6bd4\u7387<\/strong>\uff1a<\/p>\n<p class=\"has-text-align-center\">\u534a\u6b63\u5f26\u89d2\uff1a1 \u2013 cos (\u03b1) = 2 sin\u00b2 (\u03b1\/2)\uff1b sin\u00b2 (\u03b1\/2) = (1 \u2013 cos (\u03b1)) \u00f7 2<\/p>\n<p class=\"has-text-align-center\">\u534a\u89d2\u4f59\u5f26\uff1a1+cos(\u03b1)=2cos\u00b2(\u03b1\/2)\uff1b cos\u00b2 (\u03b1\/2) = (1 + cos (\u03b1)) \u00f7 2<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Razones_trigonometricas_del_angulo_triple\">\u4e09\u89d2\u7684\u4e09\u89d2\u6bd4<\/span><\/h2>\n<p>\u5728\u5177\u6709<strong>\u4e09\u89d2\uff083\u03b1\uff09<\/strong>\u7684\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528\u67d0\u4e9b\u6052\u7b49\u5f0f\u6765\u8ba1\u7b97\u5b83\u4eec\u7684\u4e09\u89d2\u6bd4\u3002\u8fd9\u4e9b\u6052\u7b49\u5f0f\u6765\u81ea\u4ee5\u4e0b\u5df2\u7ecf\u89e3\u91ca\u8fc7\u7684\u516c\u5f0f\uff1a\u53cc\u89d2\u6052\u7b49\u5f0f\u3001\u548c\u89d2\u6052\u7b49\u5f0f\u4ee5\u53ca\u4e09\u89d2\u5b66\u7684\u57fa\u672c\u6052\u7b49\u5f0f\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"311\" height=\"174\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/rapports-trigonometriques-de-langle-triple.webp\" data-src=\"\" alt=\"\u4e09\u89d2\u7684\u4e09\u89d2\u6bd4\" class=\"wp-image-7433 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p>\u4e3a\u4e86\u8bc1\u660e\u8fd9\u4e9b\u6052\u7b49\u5f0f\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u89d2\u548c\u516c\u5f0f\uff1a<\/p>\n<p class=\"has-text-align-center\">\u89d2\u5ea6\u548c\u7684\u6b63\u5f26\uff1asin (3\u03b1) = sin (\u03b1 + 2\u03b1) = sin (\u03b1) cos (2\u03b1) + sin (2\u03b1) cos (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u89d2\u5ea6\u548c\u7684\u4f59\u5f26\uff1a cos (3\u03b1) = cos (\u03b1 + 2\u03b1) = cos (\u03b1) cos (2\u03b1) \u2013 sin (\u03b1) sin (2\u03b1)<\/p>\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u5e94\u7528\u521a\u624d\u8ba8\u8bba\u7684\u8868\u8fbe\u5f0f\u4e2d\u7684\u53cc\u89d2\u516c\u5f0f\u5e76\u5e94\u7528\u4e09\u89d2\u5b66\u7684\u57fa\u672c\u6052\u7b49\u5f0f\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8bc1\u660e\u6052\u7b49\u5f0f\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u4f7f\u7528\u57fa\u672c\u4e09\u89d2\u6052\u7b49\u5f0f\u5141\u8bb8\u6211\u4eec\u5c06\u8868\u8fbe\u5f0f\u4e2d\u7684\u6240\u6709\u6bd4\u7387\u8f6c\u6362\u4e3a\u4e00\u4e2a\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u4e09\u89d2\u7684\u6b63\u5f26\u516c\u5f0f\u4ec5\u7531\u6b63\u5f26\u7ec4\u6210\uff0c\u800c\u4f59\u5f26\u7684\u516c\u5f0f\u4ec5\u5305\u542b\u4f59\u5f26\u3002\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u5b8c\u6574\u7684\u8fc7\u7a0b\uff1a<\/p>\n<p class=\"has-text-align-center\">\u4e09\u89d2\u7684\u6b63\u5f26\uff1asin(3\u03b1)=sin(\u03b1+2\u03b1)=sin(\u03b1)cos(2\u03b1)+sin(2\u03b1)cos(\u03b1)=<\/p>\n<p class=\"has-text-align-center\"> = sin (\u03b1) (cos\u00b2 (\u03b1) \u2013 sin\u00b2 (\u03b1)) + 2 sin (\u03b1) cos (\u03b1) cos (\u03b1) =<\/p>\n<p class=\"has-text-align-center\"> = sin (\u03b1) cos\u00b2 (\u03b1) \u2013 sin\u00b3 (\u03b1) + 2 sin (\u03b1) cos\u00b2 (\u03b1) =<\/p>\n<p class=\"has-text-align-center\"> = sin (\u03b1) \u00b7 (1 \u2013 sin\u00b2 (\u03b1)) \u2013 sin\u00b3 (\u03b1) + 2 sin (\u03b1) \u00b7 (1 \u2013 sin\u00b2 (\u03b1)) =<\/p>\n<p class=\"has-text-align-center\"> = sin (\u03b1) \u2013 sin3 (\u03b1) \u2013 sin3 (\u03b1) + 2 sin (\u03b1) \u2013 2 sin3 (\u03b1) =<\/p>\n<p class=\"has-text-align-center\"> = 3 sin (\u03b1) \u2013 4 sin\u00b3 (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4e09\u89d2\u4f59\u5f26\uff1a cos (3\u03b1) = cos (\u03b1 + 2\u03b1) = cos (\u03b1) cos (2\u03b1) \u2013 sin (\u03b1) sin (2\u03b1) =<\/p>\n<p class=\"has-text-align-center\"> = cos (\u03b1) (cos\u00b2 (\u03b1) \u2013 sin\u00b2 (\u03b1)) \u2013 sin (\u03b1) 2 sin (\u03b1) cos (\u03b1) =<\/p>\n<p class=\"has-text-align-center\"> = cos\u00b3 (\u03b1) \u2013 cos (\u03b1) sin\u00b2 (\u03b1) \u2013 2 cos (\u03b1) sin\u00b2 (\u03b1) =<\/p>\n<p class=\"has-text-align-center\"> = cos\u00b3 (\u03b1) \u2013 3 cos (\u03b1) sin\u00b2 (\u03b1) =<\/p>\n<p class=\"has-text-align-center\"> = cos\u00b3 (\u03b1) \u2013 3 cos (\u03b1) \u00b7 (1 \u2013 cos\u00b2 (\u03b1)) =<\/p>\n<p class=\"has-text-align-center\"> = cos3 (\u03b1) \u2013 3 cos (\u03b1) + 3 cos3 (\u03b1) =<\/p>\n<p class=\"has-text-align-center\"> = 4 cos\u00b3 (\u03b1) \u2013 3 cos (\u03b1)<\/p>\n<p>\u6700\u540e\uff0c<strong>\u4e09\u89d2\u7684\u6b63\u5207<\/strong>\u53ef\u4ee5\u901a\u8fc7\u4e24\u79cd\u65b9\u5f0f\u8ba1\u7b97\uff1a\u7b2c\u4e00\u79cd\u662f\u5c06\u6b63\u5f26\u516c\u5f0f\u9664\u4ee5\u4f59\u5f26\u516c\u5f0f\uff0c\u7b2c\u4e8c\u79cd\u662f\u5c06\u4e09\u89d2\u7684\u6b63\u5207\u8868\u8fbe\u5f0f\u4ee3\u5165\u4ee5\u4e0b\u516c\u5f0f\u6765\u8ba1\u7b97\u548c\u89d2\uff1atan (\u03b1 + 2\u03b1) = (tan (\u03b1) + tan (2\u03b1)) \u00f7 (1 \u2013 tan (\u03b1) tan (2\u03b1))\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Identidades_trigonometricas_segun_el_tipo_de_angulo\">\u6839\u636e\u89d2\u5ea6\u7c7b\u578b\u7684\u4e09\u89d2\u6052\u7b49\u5f0f<\/span><\/h2>\n<p>\u5bf9\u4e00\u7cfb\u5217\u516c\u5f0f\u8fdb\u884c\u8bc4\u8bba\u5f88\u91cd\u8981\uff0c\u8fd9\u4e9b\u516c\u5f0f\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\u662f\u5141\u8bb8<strong>\u76f4\u63a5\u5feb\u901f<\/strong>\u8ba1\u7b97\u4e09\u89d2\u6bd4\u7387\u7684\u89c4\u5219\u3002\u4e8b\u5b9e\u4e0a\uff0c\u5b83\u4eec\u4e5f\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u4e09\u89d2\u6052\u7b49\u5f0f\uff0c\u56e0\u4e3a\u5b83\u4eec\u4e0e\u6211\u4eec\u521a\u624d\u8ba8\u8bba\u7684\u6240\u6709\u8868\u8fbe\u5f0f\u5177\u6709\u76f8\u540c\u7684\u7279\u5f81\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u8fd9\u4e9b\u516c\u5f0f\u4f7f\u6211\u4eec\u80fd\u591f\u6839\u636e\u4e00\u4e2a\u89d2\u5ea6\u4e0e\u53e6\u4e00\u4e2a\u89d2\u5ea6\u7684\u5173\u7cfb\u6765\u786e\u5b9a\u8be5\u89d2\u5ea6\u7684\u4e09\u89d2\u5173\u7cfb\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u4e92\u8865\u89d2<\/h3>\n<p><strong>\u4e92\u8865\u89d2<\/strong>\uff08\u03b1 \u548c<em>\u03b2<\/em> \uff09\u7684\u603b\u548c\u7b49\u4e8e 90\u00b0\uff0c\u56e0\u6b64\u5f53\u6211\u4eec\u5c06\u5b83\u4eec\u76f8\u52a0\u65f6\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u4e00\u4e2a\u76f4\u89d2\u3002\u8981\u786e\u5b9a\u03b1\u662f<em>\u03b2<\/em>\u7684\u4f59\u89d2\uff0c\u6211\u4eec\u5fc5\u987b\u89e3\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u7684\u65b9\u7a0b\uff1a\u03b1 = 90 \u2013 <em>\u03b2<\/em> \uff0c\u5982\u679c\u8fd9\u4e2a\u7b49\u4ef7\u7684\u7ed3\u679c\u4e00\u81f4\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u65ad\u5b9a\u5b83\u4eec\u662f\u4e92\u8865\u7684\u3002\u7531\u4e8e\u8fd9\u4e9b\u6052\u7b49\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u4e00\u4e2a\u89d2\u5ea6\u4e0e\u53e6\u4e00\u4e2a\u89d2\u5ea6\u7684\u4e09\u89d2\u6bd4\u3002<\/p>\n<p class=\"has-text-align-center\">\u4f59\u89d2\u7684\u6b63\u5f26\uff1asin (90\u00b0 \u2013 \u03b1) = cos (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4f59\u89d2\u4f59\u5f26\uff1acos (90\u00b0 \u2013 \u03b1) = sin (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4f59\u89d2\u6b63\u5207\uff1atan (90\u00b0 \u2013 \u03b1) = cotan (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4f59\u89d2\u7684\u4f59\u5272\uff1a cosec (90\u00b0 \u2013 \u03b1) = sec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4f59\u89d2\u6b63\u5272\uff1asec (90\u00b0 \u2013 \u03b1) = cosec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4f59\u89d2\u7684\u4f59\u5207\uff1acotan (90\u00b0 \u2013 \u03b1) = tan (\u03b1)<\/p>\n<h3 class=\"wp-block-heading\">\u9644\u52a0\u89d2\u5ea6<\/h3>\n<p><strong>\u8865\u89d2<\/strong>\uff08\u03b1 \u548c<em>\u03b2<\/em> \uff09\u7684\u603b\u548c\u7b49\u4e8e 180\u00b0 \u6216 \u03c0 \u5f27\u5ea6\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u516c\u5f0f \u03b1 + <em>\u03b2<\/em> = 180\u00b0\u3002\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5982\u679c \u03b1 \u7684\u8865\u89d2\u4e3a<em>\u03b2<\/em> \uff0c\u5219\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u8868\u8fbe\u5f0f<em>\u03b2<\/em> = 180 \u2013 <em>\u03b1<\/em> \u3002\u7136\u540e\u4f60\u53ef\u4ee5\u770b\u5230\u6211\u4eec\u53ef\u4ee5\u4ece\u8fd9\u4e9b\u89d2\u5ea6\u63a8\u65ad\u51fa\u7684\u8eab\u4efd\u5217\u8868\uff1a<\/p>\n<p class=\"has-text-align-center\">\u8865\u89d2\u7684\u6b63\u5f26\uff1asin (180\u00b0 \u2013 \u03b1) = sin (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u9644\u52a0\u89d2\u7684\u4f59\u5f26\uff1acos (180\u00b0 \u2013 \u03b1) = -cos (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u8865\u89d2\u6b63\u5207\uff1atan (180\u00b0 \u2013 \u03b1) = -tan (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u9644\u52a0\u89d2\u7684\u4f59\u5272\uff1a cosec (180\u00b0 \u2013 \u03b1) = cosec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u8865\u89d2\u6b63\u5272\uff1asec (180\u00b0 \u2013 \u03b1) = -sec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u8865\u89d2\u4f59\u5207\uff1acotan (180\u00b0 \u2013 \u03b1) = -cotan (\u03b1)<\/p>\n<h3 class=\"wp-block-heading\">\u5171\u8f6d\u89d2<\/h3>\n<p><strong>\u5171\u8f6d\u89d2<\/strong>\uff08\u03b1 \u548c<em>\u03b2<\/em> \uff09\u662f\u90a3\u4e9b\u603b\u548c\u7b49\u4e8e 360\u00b0 \u6216 2\u03c0 \u5f27\u5ea6\u7684\u89d2\uff0c\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u6211\u4eec\u53ef\u4ee5\u63a8\u5bfc\u51fa\u516c\u5f0f \u03b1 + <em>\u03b2<\/em> = 360\u00b0\u3002\u6839\u636e\u7b2c\u4e00\u4e2a\u516c\u5f0f\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5176\u4e2d\u4e00\u4e2a\u89d2\u5ea6\u7528\u53e6\u4e00\u4e2a\u89d2\u5ea6\u8868\u793a\u5982\u4e0b\uff1a\u03b1 = 360\u00b0 \u2013 <em>\u03b2<\/em>\u6216<em>\u03b2<\/em> = 360\u00b0 \u2013 \u03b1\u3002\u73b0\u5728\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u5171\u8f6d\u89d2\u7684\u76f8\u7b49\u6027\uff1a<\/p>\n<p class=\"has-text-align-center\">\u5171\u8f6d\u89d2\u7684\u6b63\u5f26\uff1asin (360\u00b0 \u2013 \u03b1) = \u2013 sin (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5171\u8f6d\u89d2\u7684\u4f59\u5f26\uff1acos (360\u00b0 \u2013 \u03b1) = cos (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5171\u8f6d\u89d2\u6b63\u5207\uff1atan (360\u00b0 \u2013 \u03b1) = \u2013 tan (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5171\u8f6d\u89d2\u7684\u4f59\u5272\uff1a cosec (360\u00b0 \u2013 \u03b1) = \u2013 cosec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5171\u8f6d\u89d2\u7684\u6b63\u5272\uff1asec (360\u00b0 \u2013 \u03b1) = sec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5171\u8f6d\u89d2\u7684\u4f59\u5207\uff1acotan (360\u00b0 \u2013 \u03b1) = \u2013 cotan (\u03b1)<\/p>\n<h3 class=\"wp-block-heading\">\u5bf9\u89d2<\/h3>\n<p><strong>\u5bf9\u89d2<\/strong>\u6216<strong>\u8d1f\u89d2<\/strong>\uff08\u03b1 \u548c<em>\u03b2<\/em> \uff09\u662f\u5177\u6709\u76f8\u540c\u6570\u503c\u4f46\u7b26\u53f7\u4e0d\u540c\u7684\u89d2\uff0c\u6b64\u7c7b\u89d2\u7684\u793a\u4f8b\u4e3a 30\u00b0 \u548c -30\u00b0\u3002\u5e94\u8be5\u8bb0\u4f4f\uff0c\u8d1f\u53f7\u8868\u793a\u987a\u65f6\u9488\u65cb\u8f6c\uff0c\u800c\u6b63\u53f7\u8868\u793a\u9006\u65f6\u9488\u65cb\u8f6c\u3002<\/p>\n<p class=\"has-text-align-center\">\u5bf9\u89d2\u7684\u6b63\u5f26\uff1asin (-\u03b1) = \u2013 sin (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5bf9\u89d2\u4f59\u5f26\uff1acos(-\u03b1) = cos(\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5bf9\u89d2\u6b63\u5207\uff1a tan (-\u03b1) = \u2013 tan (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5bf9\u89d2\u4f59\u5272\uff1a cosec (-\u03b1) = \u2013 cosec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5bf9\u89d2\u6b63\u5272\uff1asec (-\u03b1) = sec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u5bf9\u89d2\u4f59\u5207\uff1acotan (-\u03b1) = \u2013 cotan (\u03b1)<\/p>\n<h3 class=\"wp-block-heading\">\u4e0e 90\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u6216\u6b63\/\u8d1f \u03c0\/2 \u7684\u89d2\u5ea6<\/h3>\n<p><strong>\u76f8\u5dee 90\u00b0 \u7684\u89d2\u5ea6<\/strong>\u6216<strong>\u89d2\u5ea6\u52a0\/\u51cf \u03c0\/2<\/strong> \uff08\u03b1 \u548c<em>\u03b2<\/em> \uff09\u662f\u76f8\u5dee 90\u00b0 \u7684\u89d2\u5ea6\u3002\u56e0\u6b64\uff0c\u5b83\u4eec\u53ef\u4ee5\u8868\u793a\u4e3a<em>\u03b2<\/em> \u2013 <em>\u03b1<\/em> = 90\u00b0\uff0c\u5176\u4e2d<em>\u03b2<\/em>\u6bd4<em>\u03b1<\/em>\u5927 90\u00b0\u3002\u8fd9\u4e9b\u89d2\u5ea6\u8fd8\u6709\u4e00\u7cfb\u5217\u4e0e\u4e24\u4e2a\u89d2\u5ea6\u7684\u4e09\u89d2\u6bd4\u76f8\u5173\u7684\u516c\u5f0f\u3002<\/p>\n<p class=\"has-text-align-center\">\u4e0e 90\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u6b63\u5f26\uff1asin (90\u00b0 + \u03b1) = cos (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4e0e 90\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u4f59\u5f26\uff1a cos (90\u00b0 + \u03b1) = -sin (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4e0e 90\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u6b63\u5207\uff1a tan (90\u00b0 + \u03b1) = \u2013 cotan (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4e0e 90\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u4f59\u5272\uff1a cosec (90\u00b0 + \u03b1) = sec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4e0e 90\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u6b63\u5272\uff1a sec (90\u00b0 + \u03b1) = -cosec (\u03b1)<\/p>\n<p class=\"has-text-align-center\">\u4e0e 90\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u4f59\u5207\uff1a cotan (90\u00b0 + \u03b1) = -cotan (\u03b1)<\/p>\n<h3 class=\"wp-block-heading\">\u4e0d\u540c\u4e8e 180\u00b0 \u7684\u89d2\u5ea6\u6216\u6b63\/\u8d1f \u03c0 \u7684\u89d2\u5ea6<\/h3>\n<p><strong>\u6b63\/\u8d1f\u89d2 \u03c0<\/strong> \uff08\u03b1 \u548c<em>\u03b2<\/em> \uff09\u76f8\u5f53\u4e8e\u76f8\u5dee 180\u00b0 \u7684\u89d2\u5ea6\u3002\u56e0\u6b64\uff0c\u5b83\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8868\u793a\uff1a <em>\u03b2<\/em> \u2013 <em>\u03b1<\/em> = 180\u00b0\uff0c\u5176\u4e2d<em>\u03b2<\/em> 180\u00b0 \u5927\u4e8e<em>\u03b1<\/em> \u3002\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5411\u60a8\u5c55\u793a\u4e0e\u8fd9\u4e9b\u89d2\u5ea6\u7684\u4e09\u89d2\u6bd4\u76f8\u5173\u7684\u4e09\u89d2\u6052\u7b49\u5f0f\uff1a<\/p>\n<p class=\"has-text-align-center\">\u4e0e 180\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u6b63\u5f26\uff1asin (180\u00b0 + <em>\u03b1<\/em> ) = -sin ( <em>\u03b1<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u4e0e 180\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u4f59\u5f26\uff1a cos (180\u00b0 + <em>\u03b1<\/em> ) = -cos ( <em>\u03b1<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u4e0e 180\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u6b63\u5207\uff1a tan (180\u00b0 + <em>\u03b1<\/em> ) = tan ( <em>\u03b1<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u4e0e 180\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u4f59\u5272\uff1a cosec (180\u00b0 + <em>\u03b1<\/em> ) = -cosec ( <em>\u03b1<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u4e0e 180\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u6b63\u5272\uff1a sec (180\u00b0 + <em>\u03b1<\/em> ) = -sec ( <em>\u03b1<\/em> )<\/p>\n<p class=\"has-text-align-center\">\u4e0e 180\u00b0 \u4e0d\u540c\u7684\u89d2\u5ea6\u7684\u4f59\u5207\uff1a cotan (180\u00b0 + <em>\u03b1<\/em> ) = cotan ( <em>\u03b1<\/em> )<\/p>\n<h2 class=\"wp-block-heading\"><span id=\"Transformaciones_de_razones_trigonometricas\">\u4e09\u89d2\u6bd4\u7684\u53d8\u6362<\/span><\/h2>\n<p>\u6700\u540e\uff0c\u4e09\u89d2\u6052\u7b49\u5f0f\u5141\u8bb8\u6211\u4eec\u901a\u8fc7<strong>\u5176\u4ed6\u8fd0\u7b97<\/strong>\u6765\u8868\u8fbe\u4e00\u5b9a\u7684\u4e09\u89d2\u6bd4\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u6709\u6bd4\u7387\u4e4b\u548c\u5e76\u4e14\u5e0c\u671b\u5c06\u5176\u8868\u793a\u4e3a\u4e58\u79ef\uff0c\u5219\u53ef\u4ee5\u8bc9\u8bf8\u8fd9\u4e9b\u516c\u5f0f\u3002\u4e0d\u5e78\u7684\u662f\uff0c\u867d\u7136\u6ca1\u6709\u9488\u5bf9\u6bcf\u4e2a\u7b97\u672f\u8fd0\u7b97\u7684\u8868\u8fbe\u5f0f\uff0c\u4f46\u60a8\u53ea\u80fd\u4ece<strong>\u52a0\u6cd5\u6216\u51cf\u6cd5\u5230\u4e58\u79ef\uff0c\u53cd\u4e4b\u4ea6\u7136<\/strong>\u3002<\/p>\n<h3 class=\"wp-block-heading\">\u5c06\u52a0\u6cd5\u6216\u51cf\u6cd5\u8f6c\u6362\u4e3a\u4e58\u79ef<\/h3>\n<p>\u4e0b\u9762\u56db\u4e2a\u516c\u5f0f\u5e2e\u52a9\u6211\u4eec\u8ba1\u7b97\u4e09\u89d2\u51fd\u6570\u7684\u52a0\u6cd5\u548c\u51cf\u6cd5\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"463\" height=\"298\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/convertir-laddition-ou-la-soustraction-en-produit.webp\" data-src=\"\" alt=\"\u5c06\u52a0\u6cd5\u6216\u51cf\u6cd5\u8f6c\u6362\u4e3a\u4e58\u79ef\" class=\"wp-image-7442 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\">\u5c06\u4e58\u79ef\u8f6c\u5316\u4e3a\u52a0\u6cd5\u6216\u51cf\u6cd5<\/h3>\n<p>\u4ee5\u4e0b\u56db\u4e2a\u516c\u5f0f\u5e2e\u52a9\u6211\u4eec\u8ba1\u7b97\u4e09\u89d2\u51fd\u6570\u7684\u4e58\u79ef\uff1a <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"488\" height=\"276\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/transformer-le-produit-en-addition-ou-soustraction.webp\" data-src=\"\" alt=\"\u5c06\u4e58\u79ef\u8f6c\u5316\u4e3a\u52a0\u6cd5\u6216\u51cf\u6cd5\" class=\"wp-image-7440 lazyload\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u4e09\u89d2\u6052\u7b49\u5f0f\u662f\u4e0d\u540c\u4e09\u89d2\u51fd\u6570\u4e4b\u95f4\u7684\u7b49\u5f0f\u3002\u7531\u4e8e\u8fd9\u4e9b\u4e09\u89d2\u7b49\u4ef7\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u4efb\u4f55\u5176\u4ed6\u4e09\u89d2\u6bd4\u63a8\u5bfc\u51fa\u67d0\u4e2a\u4e09\u89d2\u6bd4\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u7406 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e4%b8%89%e8%a7%92%e6%81%92%e7%ad%89%e5%bc%8f\/\"> <span class=\"screen-reader-text\">\u4ec0\u4e48\u662f\u4e09\u89d2\u6052\u7b49\u5f0f\uff1f<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[28,9],"tags":[],"class_list":["post-127","post","type-post","status-publish","format-standard","hentry","category-28","category-9"],"yoast_head":"<!-- This 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